Which of the following is true regarding probability?
I. 0 < P(E) < 1: the probability of an event E is a number between 0 and 1, exclusive.
II. The sum of the probabilities of any group of mutually exclusive events equals 1.
III. 0 <= P(E) <= 1: the probability of an event E is a number between 0 and 1, inclusive.
Click on the arrows to vote for the correct answer
A. B. C. D.A
III only is true: 0 <= P(E) <= 1: the probability of an event E is a number between 0 and 1, inclusive. A probability can equal 1 or 0; thus, statement I is false.
Statement II would only be true if it read: The sum of the probabilities of any group of mutually exclusive and exhaustive events equals 1. Throwing a 6-sided die can lead to 6 different outcomes, each of which has probability of 1/6. However, If your group of mutually exclusive outcomes only included results 1 and 2, then the sum of those probabilities is not 1. Such a group would not be exhaustive because it excludes the outcomes 3, 4, 5, 6.